First, a bit on the origins and the timing of the Rogation days generally:
The Rogation Days are the 25th of April, called Major, and the three days before the feast of the Ascension, called Minor. The Major Rogation, which has no connexion with the feast of St. Mark (fixed for this date much later) seems to be of very early date and to have been introduced to counteract the ancient Robigalia, on which the heathens held processions and supplications to their gods. St. Gregory the Great (d. 604) regulated the already existing custom. The Minor Rogations were introduced by St. Mamertus, Bishop of Vienne, and were afterwards ordered by the Fifth Council of Orléans, which was held in 511, and then approved by Leo III (795-816).
-- The Catholic Encyclopedia, "Rogation Days"
Fr. Francis X. Weiser, S.J., further notes the following on the origins of the minor rogation days:
In 470 , during a time of unusual calamities (storms, floods, earthquakes), Bishop Mamertus of Vienne in Gaul originated an annual observance of penitential exercises for the three days before the Feast of the Ascension. With the cooperation of civil authorities he decreed that the faithful abstain from servile work and that this triduum be held as a time of penance, with prayer and fasting. He also prescribed penitential processions (litanies) for each one of the three days. Thus the name "litanies" was given to the whole celebration.
Very soon other bishops of Gaul adopted the new observance. At the beginning of the sixth century it started spreading into neighbouring countries. In 511 the Council of Orleans prescribed it for the Frankish (Merovingian) part of France. The Diocese of Milan accepted the litanies, but held them in the week before Pentecost. In Spain they were observed in the sixth century during the week after Pentecost. The Council of Mainz (813) introduced them to the German part of the Frankish empire... Charlemagne and the Frankish bishops, however, urged Pope Leo III (816) to incorporate these litanies into the Roman liturgy. The pope finally consented to a compromise: the observance of the fast was rescinded, but the penitential procession was approved.
-- Handbook of Christian Feasts and Customs, p. 41-42
As for the liturgical aspect connected with rogation days, the Catholic Encyclopedia notes:
The order to be observed in the procession of the Major and Minor Rogation is given in the Roman Ritual, title X, ch. iv. After the antiphon "Exurge Domine", the Litany of the Saints is chanted and each verse and response is said twice. After the verse "Sancta Maria" the procession begins to move. If necessary, the litany may be repeated, or some of the Penitential or Gradual Psalms added. For the Minor Rogations the "Ceremoniale Episcoporum", book II, ch. xxxii, notes: "Eadem serventur sed aliquid remissius". If the procession is held, the Rogation Mass is obligatory, and no notice is taken of whatever feast may occur, unless only one Mass is said, for then a commemoration is made of the feast. An exception is made in favour of the patron or titular of the church, of whom the Mass is said with a commemoration of the Rogation. The colour used in the procession and Mass is violet. The Roman Breviary gives the instruction: "All persons bound to recite the Office, and who are not present at the procession, are bound to recite the Litany, nor can it be anticipated".